wbhart

8 ms·

1.
by wbhart 1y ago
I have not been working on formalization but theorem proving, so I can't confidently answer some of those questions. However, I recognise that there is not so much training data for LLMs wanting to use the Lean language. Moreover, you
2.
by wbhart 1y ago
Lean is an interactive prover, not an automated prover. Last year a lot of human effort was required to formalise the problems in Lean before the machines could get to work. This year you get natural language input and output, and much fast
3.
by wbhart 1y ago
1. Correct 2. Correct, however you can use Waksman as a basecase and always beat Strassen (though it is not asymptotically better of course). 5. Possible, but even so, there is already an algorithm that will work with 46 real multiplication
4.
by wbhart 1y ago
Z_2 has characteristic 2, not 0.
5.
by wbhart 1y ago
As already noted in a post by fdej further down, Waksman's algorithm from 1970, which works over the complex numbers, requires only 46 multiplications (and I guess, divisions by 2, which may or may not be relevant depending on your act
6.
by wbhart 1y ago
There's even an Open Source implementation of Waksman's in Flint, the package fdej maintains.
7.
by wbhart 1y ago
I've been using MartyPC for a few years and except for emulating glitches in hardware which depend on the manufacturer, date of manufacture or even temperature, it is getting harder to find cycle accurate tricks that MartyPC can't
8.
by wbhart 2y ago
This blog article is written in a very engaging way. It seems to be more or less a masterclass on how to keep someone's attention, although there is no meta-story making you wait for the big fulfillment at the end. I think it is the sh
9.
by wbhart 2y ago
This is an interesting article, but the absence of simple examples of theories and their toposes and invariants made it seem a little abstract. Surely if the technique is so powerful, there ought to be easy examples of it aplenty.
10.
by wbhart 3y ago
I doubt that he was intending a burn here. He's not talking about user interface issues or the like. He's most probably, I would assume, talking about the well-known issue that formalisation tools require knowledge that a standard
11.
by wbhart 3y ago
The field is fairly new to me. I'm originally from computer algebra, and somehow struggling into the field of ATP. The most interesting papers to me personally are the following three: * Making higher order superposition work. https:&
12.
by wbhart 3y ago
Yes, there are various approaches like tree-of-thought. They don't fundamentally solve the problem because there are just too many paths to explore and inference is just too slow and too expensive to explore 10,000 or 100,000 paths jus
13.
by wbhart 3y ago
Sure, but people have already applied deep learning techniques to theorem proving. There are some impressive results (which the press doesn't seem at all interested in because it doesn't have ChatGPT in the title). It's reall
14.
by wbhart 3y ago
People have done experiments trying to get GPT-4 to come up with viable conjectures. So far it does such a woefully bad job that it isn't worth even trying. Unfortunately there are rather a lot of issues which are difficult to describe
15.
by wbhart 3y ago
How on earth could you evaluate the scaling path with too little information. That's my point. You can't possibly know that a technology can solve a given kind of problem if it can only so far solve a completely different kind of
16.
by wbhart 3y ago
I think maybe I didn't make myself quite clear here. There are already algorithms which can solve advanced mathematical problems 100% reliably (prove theorems). There are even algorithms which can prove any correct theorem that can be
17.
by wbhart 3y ago
There are certainly efforts along the lines of what you suggest. There are problems though. The number of backtracks is 10^k where k is not 2, or 3, or 4..... Another issue is that of autoformalisation. This is the one part of the problem w
18.
by wbhart 3y ago
I've tested GPT-4 on this and it can be induced to give up on certain lines of argument after recognising they aren't leading anywhere and to try something else. But it would require thousands (I'm really under exaggerating h
19.
by wbhart 3y ago
I feel very comfortable saying, as a mathematician, that the ability to solve grade school maths problems would not be at all a predictor of ability to solve real mathematical problems at a research level. The reason LLMs fail at solving ma
20.
by wbhart 3y ago
The tendency to begin summarising is very annoying. I'd assumed it was because of limited attention span of human raters who rated summarised or shorter outputs more highly. And I'd assumed this had been there from the beginning.
21.
by wbhart 3y ago
One mildly good thing to say about Loeb is that he spoke out very harshly about the quantum woo that the UAP "whistleblower" David Grusch invoked to potentially explain how aliens got here without travelling great distances (somet
22.
Old Chips, New Glitches: The CGA/CRTC “Phantom” VSync(int10h.org)
4 points by wbhart 3y ago|0 comments
23.
by wbhart 4y ago
The new 4x4 matrix multiplication over F_2 has practical applications as many matrix operations over F_2 can be reduced to matrix multiplication. For anyone looking for the algorithm itself, it is actually given in in one of the extended da
24.
by wbhart 4y ago
Technically it all runs in 500kb I think (not sure if this includes DOS). And this was intentional because the guys had in mind what people would typically have available. However I think everyone is going to have to temper expectations reg
25.
by wbhart 4y ago
Actually the RAM was expanded in this demo out to 640kb. This was necessary for some of the effects in combination with the loader. Such expansion boards were available back in the day.
26.
Pushing the limits of floppy disk boot sectors: sectorLISP(youtube.com)
3 points by wbhart 5y ago|0 comments
27.
by wbhart 5y ago
According to an article on PubMed, that's largely a myth, based on early, faulty studies [1]. [1] "Low incidence of cardiovascular disease among the Inuit--what is the evidence?"
28.
by wbhart 6y ago
I'd expect within seconds that Google is alerted of a very large number of issues with their servers and that the status page would be updated (the green light going to red) within seconds. It's now quite some time after the start
29.
by wbhart 6y ago
There's a lot of us here due to the University. I know some of them personally.
30.
by wbhart 6y ago
I'm on the west yes. But you don't hear planes? It's a constant conveyor belt, even across the city!

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